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Dear Colleagues,
I suspect that one of Professor Zadeh's motivations in this recent thread was to explore the relationship between formal and ordinary logic. Else why would he have invited P. Tillers – a person largely innocent of deep knowledge about modern logic -- to give his opinion about the chestnut that he (Prof. Zadeh) concocted?
The relationship between uncertain legal reasoning and formal mathematical reasoning about uncertainty has a history that runs back to the dawn of modern probability theory in the 17th and 18th centuries. Attention (on the legal side) to mathematical accounts of uncertainty has waxed and waned over the centuries. Mostly it has waned. In the last 35 years, however, there has been a renaissance in my field -- in the law of evidence and [factual] proof – there has been renaissance of efforts to use formal logic and mathematics to portray and possibly even to regulate factual inference and factual proof in litigation. Two of the key advocates of this sort of enlightenment have been David Kaye of Arizona State College of Law and Richard Lempert of Michigan Law School (and presently head of NSF’s division of social sciences). Another important advocate of mathematical analysis of evidential argument in law has been David Schum, who is at George Mason’s School of Information Technology and Engineering, and who also does some occasional teaching at the law school there and also at University College London.
The effort during the last 35 to use probability theory to study factual inference in litigation has been embroiled in seemingly-endless controversies and debates. Proposals to put matters such as Bayes Theorem directly before juries have been criticized and, yes, ridiculed. And, even though a lot formal reasoning about uncertainty is now getting into trials and litigation through the back door -- via scientific evidence --, the judiciary and, by and large, academic lawyers have roundly rejected efforts to put probability theory (and formal statistical methods) in the hands of judges and jurors with the idea that judges and jurors use such formal methods to analyze and assesses and improve their own "ordinary" judgments about factual questions that are "ordinary," that do not clearly fall within some scientific field.
But much of the controversy over "trial by mathematics" (which Professor Laurence Tribe – yes, the renowned constitutional law scholar -- helped launch in 1982 with his tenure piece) has been deeply muddled because many of the combatants have not been clear about what they think formal probability theory in trials is or might be for -- or, in any event, the legal combatants over the use of formal probability theory in trials have regularly misunderstood the opposing camp's objections and concerns. Professor Zadeh's riddle, it seems to me (for my purposes, in any event), resurrects the general question of the purpose(s) of formal accounts of matters such as evidential reasoning in law. I hope to explore this question a bit at a conference in Berkeley in November.
Let me, at this point, suggest just a few of the many different purposes one might attach to the project of "formalizing" argument about matters such as factual issues in litigation. (I am particularly interested in argument about "non-scientific" factual issues, i.e., questions that for the time being do not seem to fall within the superior expertise of some apparently valid specialized body of knowledge that uses rigorous methods such as explicit mathematical reasoning.)
Here is a list of possible purposes:
1. One might try to devise methods just to predict how judges and jurors will resolve factual issues in litigation.
2. One might try to devise methods that might replace existing methods of argument and deliberation about factual questions in legal settings.
3. One might try to devise methods of analysis that mimic conventional methods of argument about evidence in legal settings.
4. This objective is close to the third objective: One might try to devise methods that mathematically illiterate judges and jurors might employ to make more effectively -- or "better" -- the kinds of arguments they presently make. So in this instance newly-devised methods are to support or facilitate existing or ordinary argument and deliberation in litigation.
5. One might try to devise methods that would capture some but not all ingredients of conventional argument in litigation about factual questions -- e.g., to capture the ordinary or usual meaning or sense or reference of a notion such as "red light" or "yellow caution signal."
6. One might try to develop forms of argument that are somehow "immanent" in ordinary reasoning about uncertain propositions – in order to give ordinary reasoners in law [non-scientists etc.] tools that seem appropriate to the way those ordinary people reason and, possibly, the way they "ought" to reason. (This objective is reminiscent of #4 but it may also be a bit different.)
7. One might just want to understand better how actors such as jurors and judges reason; one’s aim here might be a kind of 19th century Germanic desire to know just for the sake of knowing, for the sake of Wissenschaft and Erkenntnis alone – and let the devil take the hindmost.
Now this taxonomy (above) is not elegant and it is not complete. But it gives a hint of the complexity and difficulty -- from this American legal academic's vantage point -- of the relationship between formal logical and explicitly mathematical argument about matters such as factual issues in litigation, on the one hand, and the methods of argument that are now used (and have been used for centuries) about such questions in legal settings, on the other hand. Once some this general question is fleshed out a bit better, the road to a more clear-headed assessment of the possible contributions of fuzzy set theory, fuzzy logic, soft computing, and the nascent generalized theory of uncertainty may be open.
I am definitely not the person to do a comparative evaluation of the possible contributions of conventional probability theory and fuzzy sets, etc., for the analysis or management of uncertain inference and proof in legal settings. But it is possible that sound comparative analysis can be done properly only if future protagonists who are in fields other than law have a decent understanding of how existing argument about factual propositions works in legal settings.
§ One good way to start to get a handle on this – on how lawyers and legal systems handle uncertain factual inference and inconclusive. Ambiguous, and incomplete evidence – is, I think, to read James Franklin's sprawling but magnificent book THE SCIENCE OF CONJECTURE: EVIDENCE AND PROBABILITY BEFORE PASCAL (Johns Hopkins, 2002), http://www.press.jhu.edu/books/title_pages/2844.html. This book, written by a firm proponent of Bayesian methods, is interesting in part because it defends to a very substantial extent informal non-Bayesian methods of argument that Franklin thinks have characterized reasoning in legal settings about factual questions for two thousand years or so. (Nonetheless, there is not much reason to think that Franklin approves of fuzzy logic and similar methods, is there?)
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My remarks (above) were (as always) hastily-composed -- and for that I must apologize. But I thought that, on balance, my hastily-composed remarks would be more useful than harmful -- and so I pass them along.
Sincerely,
Peter T
-----Original Message-----
The answer is: No, it isn't. Of the many respondents, only a few came up with what in my view is a correct analysis. Here is my analysis. Starting with the proposition p: Ronald was born in New York, following one line of reasoing leads to the conclusion r: It is possible that Ronald was born in New Jersey. Another line of reasoning leads to the conclusion s: It is not possible that Ronald was born in New Jersey. The question boils down to: Are r: It is possible that Ronald was born in New Jersey, and s: It is not possible that Ronald was born in New Jersey, contradictory?
The answer depends on how r: It is not possible that Ronald was born in New Jersey, is parsed. If r is parsed as: It is not (possible that Ronald was born in New Jersey), then there is contradiction. On the other hand, if r is parsed as: It is (not possible) that Ronald was born in New Jersey--which is how r should be parsed--then there is no contradiction since r is equivalent to t: Ronald was not born in New Jersey, and there is no contradiction between t: Ronald was not born in New Jersey, and s: It is possible that Ronald was born in New Jersey. This follows from the observation that, for any proposition v, possible u is equivalent to v or not v.
How would the issue under consideration be dealt with by someone, say X, who is conversant with legal reasoning but has no familiarity with formal logic? In this connection, I should like to pose a question to our eminent legal expert Professor Tillers.
Suppose that in the course of a trial for murder, witness A testifies that p: It is not possible that Y committed the murder, while witness B testifies that q: It is possible that Y committed the murder. Would X consider p and q to be contradictory? My inclination is to feel that most X's would view p and q as being contradictory.
Warm regards to all,
Lotfi
-- Lotfi A. Zadeh Professor in the Graduate School, Computer Science Division Department of Electrical Engineering and Computer Sciences University of California Berkeley, CA 94720 -1776 Director, Berkeley Initiative in Soft Computing (BISC) _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai |
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